首先詳述非相對論性量子力學之基本散射理論，並以此為基礎，討論一模型模擬均勻粒子束入射另一吸附於平滑金屬表面之粒子的散射過程。此模型為將粒子間交互作用平均位勢置於一完全光滑反射而不可入侵之表面，並以均勻且內無交互作用之粒子束入射其上，然後以量子力學原理討論其散射情形。由於此模型中表面的不可入侵性，將此散射過程稱為表面或半空間量子散射。利用此表面不可入侵之邊界條件，得到相異於全空間散射的能量本徵態在遠端的漸近形式，再與分波解析之結果對照而得到其明確的解析形式，該形式給出了微分散射截面以及總散射截面的公式。續乃以數值方法，實際考慮一些理想或較為實際之交互作用平均勢，以先前推論得到之公式計算微分散射截面以及總散射截面。

§1 緒論 1

§2 理論 3
2.1量子散射理論 3
A. 粒子入射之動圖像…………………………………………………3
B. 粒子均勻入射之靜圖像………………………………………...17
C. 散射截面………………………………………………………...19
D. 球對稱位能之分波解析…………………………………………..21
E. 相移之計算……………………………………………………...27
2.2 表面量子散射理論 29
A. 硬牆反射…………………………………………………………..29
B. 表面散射截面…………………………………………………...35

§3 結果與討論 41
3.1 硬球的全空間與半空間散射計算 41
A. 總截面……………………………………………………………..41
B. 微分截面………………………………………………………...45
3.2 討論 65
A. 總截面……………………………………………………………..65
B. 微分截面…………………………………………………………...69

§4 結論 75
§5 附錄 77
A. 自由粒子波包……………………………………………………..73
B. 不依時薛定諤方程的積分形式………………………………...77
C. 散射截面…………………………………………………………81

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